What is ‘normality’? Conditional and unconditional interpretation

One of the central ideas behind our approach is to treat separately and differently the ‘normal’ and the exceptional parts of the return distribution. The idea seems natural enough and, at least in principle, well defined. However, defining what we mean by the ‘normal’ part of the distribution is not quite as straightforward as it may at first glance appear. In order to illustrate where the problems lie, we are going to use in this chapter much longer time series than those we employ in the part of the book devoted to asset allocation. In particular, in this chapter we are going to use as our data set 3360 × 4 daily returns, covering the period February 1997 to June 2010 for three asset classes: Government Bonds, Investment-Grade Credit Bonds, and Equities (called asset class Bond, Credit and Equity, respectively, in the following). More precisely, the following indices were used:

1. for Bond the BarCap US Treasury Index;

2. for Credit the BarCap US Credit Index;

3. for Equity the S&P 500.

To understand where our problem lies, let us look at Figures 17.1–17.4, which display two pairs of time series. Each pair displays the rolling pairwise correlation between the same two asset classes, in one case using the whole data set, in the other just the ‘normal’ portion of the data. The time series we look at are Bonds, Credit and Equities.